The face-mounted resonator was described by Newell in 1964 and consisted of a piezo-active resonator surmounting a stack of quarter-wavelength layers of alternating acoustic impedance that was bonded to a robust substrate. The most important feature of that configuration was mechanical impedance at the resonator mounting surface that approximated a short circuit so as to maintain high resonator quality factor (Q) values. Despite encouraging preliminary experimental results, the necessary microfabrication technologies were not available. Recent advanced fabrication modalities have led to more modern realizations of the face-mounted resonator, which are now known as the solidly-mounted resonator (SMR).
Acoustic stack plates in SMRs have been used only for their mechanical properties as impedance transformers, but stacks with a piezoelectric layer provide an additional degree of freedom, because the electrical boundary condition on the piezoelectric layer may be altered. FIG. 1 schematically depicts several stacked layers of a prior art SMR. The stacked layers perform in a manner similar to a Bragg antireflective coating used on camera lenses. But instead of alternating layers with high and low indices of refraction, the stack consists of alternating layers of high and low acoustic impedance materials. However, having alternating layers is not enough. The necessary condition is that at the frequency of interest each layer needs to be approximately ¼ of a wavelength thick.
Each stacked layer can be considered an acoustic transmission line (TL) able to transform any impedance attached to one end, so that when looking into the other TL end, one sees different impedance. If an impedance ZT, where subscript “T” is termination, is attached to one end of a TL having a characteristic impedance Zo, then looking into the other end of the TL, one sees an input impedance given by the following expression:Zinput=Zo[ZT+jZo tan(θ)]/[Zo+jZT tan(θ)]; θ=(2πfl)/v,  Equation (1)where “f” is the operating frequency, “l” is the geometrical thickness of the layer, “v” is the acoustic velocity in the layer, and the wavelength is λ=v/f.
When the TL is of negligible length, l is approximately zero, so θ and tan(θ) are about zero. In this case, Zinput is about ZT. But where frequency is such that l is approximately λ/4, then θ will be about π/2, tan(θ) will be very large, and the two tangents will cancel out, leaving Zinput about equal to Zo2/ZT. Thus, in the vicinity of this particular frequency, the input impedance will change from ZT to Zo2/ZT.
The transformation taking place when the stack consists of alternating layers of high (ZH) and low (ZL) impedance values, and each is about λ/4 thick, results in an input mechanical impedance at the face of the resonator of approximately [ZL(ZL/ZH)N], where N is the number of pairs of layers. This means that the bonded face of the resonator “sees” very low acoustic impedance. A low value of acoustic impedance, which approximates a mechanical short circuit, means that the resonator face is substantially traction-free, and decoupled from the layers and substrate. This type of resonator is unable to radiate any acoustic power down the stack and into the substrate; so that virtually all energy is reflected back into the resonator, which should leave the ideal situation of an undiminished Q. Theoretically, the only source of loss is the loss within the resonator itself; for low acoustic loss materials, this is quite small, and high Q values could be realized. However, such benefits remain largely theoretical and have not yet been reliably and routinely attained in manufacturing, largely due to the inability to insure the λ/4 thick wavelength condition at the single operating frequency.
The prior art stacked piezoelectric SMR has not realized its full potential for several reasons, including manufacturing limitations and the fact that devices that use resonators operate over a range of frequencies. Manufacturing difficulties make it infeasible for all layers to have exactly the same acoustic length; those skilled in the art realize that there will always be some fabrication deviations from the ideal, leading to suboptimal performance. Inasmuch as devices using resonators, such as filters, operate over a range of frequencies, even if the stack layers are λ/4 thick at one frequency, they cannot be at any other frequency, since λ=v/f, because as frequency changes, so does λ.
Thus, there has been a long-felt need for an SMR configuration that can overcome and obviate the prior art manufacturing limitations and the disadvantages and shortcomings of leakage and an unwanted frequency shift.